No. This is neither safe, nor effective.
You mean a switch-mode power supply (SMPS) and yes, that's what this is. This means that incoming AC is rectified and buffered by one or two fairly large caps, usually in the 100-500uF range. 160V at this capacitance is a very, very nasty jolt and if you're unlucky, lethal.
In an SMPS, this high-voltage DC is switched to feed the primary of a step-down transformer. The switching element is generally a MOSFET, usually discrete component in TO220 or similar form factor. To handle with the switching losses, this MOSFET is heatsinked. Depending on the construction of the power supply, this entire heatsink may float at high voltage. Furthermore, in many power supplies, part of the frame/housing is used as a heatsink; in these cases there should be an insulator pad between the switching transistor (and usually rectifier diodes) and the heatsink/casing, but don't bet any money on this being (1) the case and (2) effective; I have in fact worked on units where assembly errors had these pads mounted improperly putting the housing of the power supply on HVDC (in this case it was fortunately sitting inside a plastic outer shell!)
Given the fact that the problem is intermittent, it's fairly sure that it's not this part that has given the ghost since MOSFETs virtually always fail hard - it's a binary thing. One moment they're fine, the next moment they're totally dead. Furthermore, they will always run warm or even quite hot in an application like this, so feeling around won't be conclusive to begin with. The heatsink is there for a reason, after all. Any browning on the PCB is also not necessarily an indicator of a defect since over the course of 10-20 years there will usually be discoloration of the PCB and some components in hot areas.
Visual inspection can give some clues. In cases of hard faults, look for the EMI capacitor right at the AC input which tends to pop after a decade or so; this is generally a little (usually yellow) box. They generally fail catastrophically; i.e. they explode (but won't start a fire while doing so if the correct type was used), so it's easy to see if this has happened. A more likely candidate in this case is/are the HV buffer capacitor(s) immediately after the rectifier; these are generally brown or black cylinders and the largest components on the PCB together with the transformer and any heatsinks. Check for bulging or leakage of the electrolyte. Given the nature of the problem, this is the place where I'd personally start; it would make for a relatively quick & easy fix. This inspection would still involve handling the unit with the utmost care because such a large part of it can still float at 160VDC (in 230V countries it's around 325V even!) and it's really, really easy and really nasty to mistakenly touch the wrong part here and there.
Of course, any signs of obvious explosive deconstruction and/or carbonization of parts is a good clue of a defect. However, I would have expected part of the story to involve mention of smoke or at least nasty smells.
Long story short: inspection is possible, but it only makes sense if you know what you're doing and what you're looking for. In OP's case, I'd stick with the advice to take the device to someone who has experience handling electronics and preferably these scanners in particular. In any case, you don't go feeling around an SMPS with your fingers.
Thanks to koraks for pointing out the problems with my post, and I am sorry I was so sloppy about it. What was especially dumb was that most people familiar with circuitry would not poke around carelessly in high-voltage areas, but people with variable experience read these posts, so I should have been especially careful. Koraks gives great advice. I was just trying to give a hint, given the timing of the failure in the OP's scanner.
Sometimes, partial/intermittent failures are due to current leakage or oscillation or other causes, and finding a hot component that
should not be hot can give a hint to where a problem could be. I have repaired a few complex devices that would fail soon after turn-on using this approach. Another technique is to spray suspect devices with freeze-spray to cool it down and look for recovery in the circuit's function. Some people use a thermal camera to see hot spots. This avoids hot fingers but you still have to know what devices would be normally warm or even hot (say 50 degrees C).
I have a Nikon Coolscan V ED, and when it had to be repaired several years ago, I sent it to Nikon. This evening I took mine apart to see how complex it was, and there were a lot of surface-mounted devices on the main board, and it would be very time-consuming to track down a problem on it, even with a schematic, let alone fix it without special tools. There are a few large, complex integrated circuits too. I bet repairers replace the board rather than fix it.
The power supply on my Nikon scanner had no retained voltages on either the high or low voltage sections after turning it off. But it's always good to check voltages, even after the unit is turned-off, before handling it. Usually, a resistor(s) to ground drops the voltage on the caps to zero in a few seconds, but as koraks mentions, you can't count on that.
The Nikon scanner's power supply's output had 5, 5, 15, and -12 volt DC lines, which are not surprising levels. Assuming it is the same for the Nikon 8000, a skilled person could check these voltages (and ripple) to see if it was the power supply, or perhaps current leakage on the main board pulling a voltage down. The power supply could be removed and tested on its own (but it may need a load to run). But still, it would probably be better to send the whole scanner to the people that fix them, especially if the power supply is okay.
I bought the scanner used about 20 years ago, but tonight all the board surfaces and devices showed no discoloration, and the unit stays cool when I use it. It is rated at 0.3 amps at 110 VAC.
I have had switching power supplies fail slowly/intermittently, but just replaced them with similar or better units. I had one (in a CRT video monitor) behave opposite of the OP's --- I had to keep turning it off and on until the capacitors charged enough to allow the circuit to stabilize and stay on. After re-capping, it worked fine.